Universality in protein residue networks

Residue networks representing 595 nonhomologous proteins are studied. These networks exhibit universal topological characteristics as they belong to the topological class of modular networks formed by several highly interconnected clusters separated by topological cavities. There are some networks which tend to deviate from this universality. These networks represent small-size proteins having less than 200 residues. We explain such differences in terms of the domain structure of these proteins. On the other hand, we find that the topological cavities characterizing proteins residue networks match very well with protein binding sites. We then investigate the effect of the cutoff value used in building the residue network. For small cutoff values, less than 5Å, the cavities found are very large corresponding almost to the whole protein surface. On the contrary, for large cutoff value, more than 10.0 Å, only very large cavities are detected and the networks look very homogeneous. These findings are useful for practical purposes as well as for identifying "protein-like" complex networks. Finally, we show that the main topological class of residue networks is not reproduced by random networks growing according to Erdös-Rényi model or the preferential attachment method of Barabási-Albert. However, the Watts-Strogatz (WS) model reproduces very well the topological class as well as other topological properties of residue network. We propose here a more biologically appealing modification of the WS model to describe residue networks.